Scientific Collection «InterConf», (39): with the Proceedings of the 8th International Scientific and Practical Conference «Science and Practice: Implementation to Modern Society» (December 26-28, 2020) at Manchester, Great Britain

1. Digital portrait of works. 26 Latin letters indicated for all 5 languages were 
taken as accounting elements for describing the works. 
Definition 1. A digital portrait (DP) of a text is the frequency distribution of 26 
letters. 
The DP of the text 
𝑇 is written in tabular form: 

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SCIENTIFIC COLLECTION «INTERCONF» | № 3(39)
836 
𝑁 ∶ 1 2 . . . 26
𝑃 ∶ 𝑝
1
𝑝
2
. . . 𝑝
26 
,
(1) 
in which the first line is the numbers of letters arranged in alphabetical order, and the 
second is the relative frequencies of letters in the text 
𝑇, and ∑
𝑝
𝑘
26
𝑘=1
= 1. 
Simultaneously with (1), the digital portrait is also represented as a discrete function 
𝐹(𝑠) = ∑
𝑝
𝑘
𝑠
𝑘=1
(𝑠 = 1, ⋯ , 26). 
(2) 
2. Distances between digital portraits of texts. Let 
𝑇
1
, 𝑇
2
be an arbitrary pair 
of texts characterized on the basis of a single alphabet, and 
𝐹
(𝛼)
(𝑠) = ∑
𝑝
𝑘
(𝛼)
𝑠
𝑘=1
(3) 
is the corresponding DP represented by discrete functions, 
𝛼 = 1, 2, and 𝑠 = 1, ⋯ , 26. 
Definition 2. The distance between the texts 
𝑇
1
 and 
𝑇
2
 is called a positive number 
𝜌 (𝑇
1
, 𝑇
2
), determined by the formula 
 
𝜌 (𝑇
1
, 𝑇
2
) = √
26
2
𝑚𝑎𝑥
𝑠
|𝐹
(1)
(𝑠) − 𝐹
(2)
(𝑠)|. 
(4) 
3. Hypothesis 
ℍ of “homogeneity” of products. It is used in order to highlight 
the characteristic feature of texts intended for building a mathematical model for 
recognizing the language of works. We formulate it as follows. 
HYPOTHESIS 
ℍ. Works written in one language are “homogeneous”, but in 
different languages they are “not homogeneous”. 
Speaking about the “homogeneity” of works (texts), we mean their similarity, 
uniformity, affinity, kinship, etc.